Abstract
We show that the Heisenberg type group HX=(Z2⊕V){left semidirect product}V*, with the discrete Boolean group V:=C(X,Z2), canonically defined by any Stone space X, is always minimal. That is, H X does not admit any strictly coarser Hausdorff group topology. This leads us to the following result: for every (locally compact) non-archimedean G there exists a (resp., locally compact) non-archimedean minimal group M such that G is a group retract of M. For discrete groups G the latter was proved by S. Dierolf and U. Schwanengel (1979) [6]. We unify some old and new characterization results for non-archimedean groups.
Original language | English |
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Pages (from-to) | 2497-2505 |
Number of pages | 9 |
Journal | Topology and its Applications |
Volume | 159 |
Issue number | 9 |
DOIs | |
State | Published - 1 Jun 2012 |
Bibliographical note
cited By 2Keywords
- Boolean group
- Heisenberg group
- Isosceles
- Minimal group
- Non-archimedean group
- Stone duality
- Stone space
- Ultra-metric